Due to the importance of these models, there are many theoretical and algorithmic studies on each of these models [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. For the truncated quadratic model, the graduated non-convexity algorithm was proposed in [2]} and see [13]}, [9]} for recent developments. Difference of convex algorithm (DCA) [8]}, preconditioned DCA [16]}, and the first-order primal-dual algorithm [11]} are also developed for the truncated quadratic models. For the German-McClure model, Hebert-Leahy model, and Ambrosio-Tortorelli model, there are also lots of analysis and algorithmic developments; see [1]}, [19]}, [20]}, [3]}, [22]} and so on.
